The present disclosure relates generally to seismic processing, and more particularly to an apparatus and method for using well log data to augment seismic data.
Subsurface formations are typically mapped, e.g., for oil and gas exploration, using seismic survey techniques. When acoustic energy is launched into the earth, subsurface acoustic reflections occur at transition points in acoustic impedance, which generally correlate to boundaries between strata with different features. Although a variety of seismic energy sources and seismic detectors are common, the basic principle of seismic survey techniques involves launching one or more acoustic waves downward into the earth and listening at known locations at or near the earth's surface for reflections of these waves from subsurface features. A seismic trace is generally created for each seismic detector for each seismic energy source activation.
Generally, multiple seismic source and detector locations are selected so that a view of subsurface formations can be reconstructed in a subsurface cross-section or in a three-dimensional survey area. Various techniques exist for stacking multiple seismic traces and using multiple traces to reject multiple reflections and/or noise in a seismic trace, thereby creating processed seismic trace data that provides a more useful mapping of underground features.
Some seismic survey data error sources are difficult to correct without additional data. For instance, errors in modeled acoustic velocity tend to reduce the resolution of stacked data. The resolution of the stacked data thus can be improved when actual underground observations can be gathered, e.g., along the bore of a well at the location of a seismic trace, using sensors lowered into the well. The sensors measure, directly or indirectly as a function of depth, features such as the sound velocity in the rock around the well bore, the density of the rock, rock porosity, liquid saturation, acoustic impedance, and reflectivity. The well data is commonly referred to as a well log.
One established technique for matching seismic data to well logs is to calculate and apply simple matching filters. When following this approach, one minimizes the residual error between the filtered trace and a nearby reflectivity well log. This is done in the least squares sense by adjusting coefficients of the filter such that the filtered seismic trace at the well approximates the well log. Mathematically, this is accomplished by minimizing the function
                    U        =                              ∑                          i              =              1                        N                    ⁢                                    (                                                R                  i                                -                                                      ∑                                          j                      =                                              -                        L                                                              M                                    ⁢                                                            F                      j                                        *                                          S                                              i                        +                        j                                                                                                        )                        2                                              (        1        )            where F is the matched filter, S is the seismic trace, R is the reflectivity log, L and M define the span of the filter, and N is the number of samples along which S is to be matched to R. In one common method, the partial derivatives of this function are taken, forming a set of linear equations that are then solved to determine the filter coefficients.
Once the filter coefficients are determined, the filter is applied to other traces in the vicinity of the well. This process is further illustrated in FIG. 1, where block 100 derives the matched filter coefficients from a seismic trace at the well and a reflectivity log of the well. Block 110 then uses these matched filter coefficients to filter other seismic traces in the vicinity of the well, producing corresponding filtered seismic data for each input seismic trace.
To further exemplify the process, FIG. 2 shows a data set 200 comprising a portion of each of a plurality of seismic traces, where the x-axis represents distance along a survey line, the y-axis represents sample time, and the z-axis (shown as left-right movement along each trace and corresponding shading) represents variations in reflectivity. This data is taken from an actual land survey, with temporal sample spacing of 1 ms.
A synthetic seismogram 210 is shown overlaid on data set 200. The synthetic seismogram 210 was derived from a well log comprising density and sound velocity as a function of depth. The acoustic impedance was calculated by multiplying the density and sound velocity at each sample point, and then synthetic reflectivity was calculated from the derivative of the acoustic impedance. As can be observed, the synthetic seismogram 210 contains much higher frequency content than the seismic traces, and thus reveals details in the vicinity of the well that are missing from the corresponding seismic trace 220, taken at the location of the well.
In a first example, a 54 ms-long matched filter was obtained by performing a least-squares fit of synthetic (i.e., well log) seismogram 210 to seismic trace 220 over the samples in the range between 2.5 and 3.05 seconds. The resulting matched filter was then run over the other seismic traces in data set 200 to create filtered reflectivity data. A recursive inversion was then performed to produce a relative impedance plot 300, a portion of which is illustrated in FIG. 3. The corresponding section of a well log acoustic impedance plot 310 is shown overlaid on plot 300, and more specifically overlying a filtered trace 320 at the location of the well. The filtered plot does not contain the high frequencies necessary to represent the detail in high-frequency events evident in the well log, e.g., those at about 2.64 and 2.92 seconds.
In a second example, the linear matched filter example was rerun at three times the filter length (162 ms) of the original example, resulting in the relative impedance plot 400 illustrated in FIG. 4. The recursive inversion of this data (e.g., filtered trace 420) matches well log acoustic impedance plot 310 better than plot 300 did, particularly at low frequencies, but does not appear to add any higher frequency content to the plot.